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        <title>API docs for &ldquo;sympy.thirdparty.mpmath.mpmath&rdquo;</title>
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        <body><h1 class="module">Module s.t.m.mpmath</h1><span id="part">Part of <a href="sympy.thirdparty.mpmath.html">sympy.thirdparty.mpmath</a></span><div class="toplevel"><div class="undocumented">Undocumented</div></div><table class="children"><tr class="class"><td>Class</td><td><a href="sympy.thirdparty.mpmath.mpmath.mpnumeric.html">mpnumeric</a></td><td><div><p>Base class for mpf and mpc. Calling mpnumeric(x) returns an mpf</p>
</div></td></tr><tr class="function"><td>Function</td><td><a href="#sympy.thirdparty.mpmath.mpmath.convert_lossless">convert_lossless</a></td><td><div><p>Attempt to convert x to an mpf or mpc losslessly. If x is an</p>
</div></td></tr><tr class="class"><td>Class</td><td><a href="sympy.thirdparty.mpmath.mpmath.context.html">context</a></td><td><div><p>Metaclass for mpf and mpc. Holds global working precision.</p>
</div></td></tr><tr class="function"><td>Function</td><td><a href="#sympy.thirdparty.mpmath.mpmath._convert">_convert</a></td><td><div><p>Convet x to mpf data</p>
</div></td></tr><tr class="class"><td>Class</td><td><a href="sympy.thirdparty.mpmath.mpmath.mpf.html">mpf</a></td><td><div><p>An mpf instance holds a real-valued floating-point number. mpf:s</p>
</div></td></tr><tr class="function"><td>Function</td><td><a href="#sympy.thirdparty.mpmath.mpmath.make_mpf">make_mpf</a></td><td><div><p>Create mpf verbatim from a given tuple of data.</p>
</div></td></tr><tr class="class"><td>Class</td><td><a href="sympy.thirdparty.mpmath.mpmath.mpc.html">mpc</a></td><td><div><p>An mpc represents a complex number using a pair of mpf:s (one</p>
</div></td></tr><tr class="function"><td>Function</td><td><a href="#sympy.thirdparty.mpmath.mpmath.make_mpc">make_mpc</a></td><td><span class="undocumented">Undocumented</span></td></tr><tr class="class"><td>Class</td><td><a href="sympy.thirdparty.mpmath.mpmath.constant.html">constant</a></td><td><div><p>Represents a mathematical constant with dynamic precision.</p>
</div></td></tr><tr class="function"><td>Function</td><td><a href="#sympy.thirdparty.mpmath.mpmath.sqrt">sqrt</a></td><td><div><p>For real x &gt;= 0, returns the square root of x. For negative or</p>
</div></td></tr><tr class="function"><td>Function</td><td><a href="#sympy.thirdparty.mpmath.mpmath.hypot">hypot</a></td><td><div><p>Returns the Euclidean distance sqrt(x*x + y*y). Both x and y</p>
</div></td></tr><tr class="function"><td>Function</td><td><a href="#sympy.thirdparty.mpmath.mpmath.ef">ef</a></td><td><span class="undocumented">Undocumented</span></td></tr><tr class="function"><td>Function</td><td><a href="#sympy.thirdparty.mpmath.mpmath.tan">tan</a></td><td><div><p>Returns the tangent of x.</p>
</div></td></tr><tr class="function"><td>Function</td><td><a href="#sympy.thirdparty.mpmath.mpmath.tanh">tanh</a></td><td><div><p>Returns the hyperbolic tangent of x.</p>
</div></td></tr><tr class="function"><td>Function</td><td><a href="#sympy.thirdparty.mpmath.mpmath.arg">arg</a></td><td><div><p>Returns the complex argument (phase) of x. The returned value is</p>
</div></td></tr><tr class="function"><td>Function</td><td><a href="#sympy.thirdparty.mpmath.mpmath.log">log</a></td><td><div><p>Returns the base-b logarithm of x. If b is unspecified, return</p>
</div></td></tr><tr class="function"><td>Function</td><td><a href="#sympy.thirdparty.mpmath.mpmath.power">power</a></td><td><div><p>Returns x**y = exp(y*log(x)) for real or complex x and y.</p>
</div></td></tr><tr class="function"><td>Function</td><td><a href="#sympy.thirdparty.mpmath.mpmath.atan">atan</a></td><td><div><p>Returns the inverse tangent of x.</p>
</div></td></tr><tr class="function"><td>Function</td><td><a href="#sympy.thirdparty.mpmath.mpmath.atan2">atan2</a></td><td><div><p>atan2(y, x) has the same magnitude as atan(y/x) but accounts for</p>
</div></td></tr><tr class="function"><td>Function</td><td><a href="#sympy.thirdparty.mpmath.mpmath._asin_complex">_asin_complex</a></td><td><span class="undocumented">Undocumented</span></td></tr><tr class="function"><td>Function</td><td><a href="#sympy.thirdparty.mpmath.mpmath.asin">asin</a></td><td><div><p>Returns the inverse sine of x. Outside the range [-1, 1], the</p>
</div></td></tr><tr class="function"><td>Function</td><td><a href="#sympy.thirdparty.mpmath.mpmath._acos_complex">_acos_complex</a></td><td><span class="undocumented">Undocumented</span></td></tr><tr class="function"><td>Function</td><td><a href="#sympy.thirdparty.mpmath.mpmath.acos">acos</a></td><td><div><p>Returns the inverse cosine of x. Outside the range [-1, 1], the</p>
</div></td></tr><tr class="function"><td>Function</td><td><a href="#sympy.thirdparty.mpmath.mpmath.asinh">asinh</a></td><td><div><p>Returns the inverse hyperbolic sine of x. For complex x, the</p>
</div></td></tr><tr class="function"><td>Function</td><td><a href="#sympy.thirdparty.mpmath.mpmath.acosh">acosh</a></td><td><div><p>Returns the inverse hyperbolic cosine of x. The value is</p>
</div></td></tr><tr class="function"><td>Function</td><td><a href="#sympy.thirdparty.mpmath.mpmath.atanh">atanh</a></td><td><div><p>Returns the inverse hyperbolic tangent of x. Outside the range</p>
</div></td></tr><tr class="function"><td>Function</td><td><a href="#sympy.thirdparty.mpmath.mpmath.rand">rand</a></td><td><div><p>Return an mpf chosen randomly from [0, 1).</p>
</div></td></tr></table>
            <div class="function">
            <div class="functionHeader">def <a name="sympy.thirdparty.mpmath.mpmath.convert_lossless">convert_lossless(x):</a></div>
            <div class="functionBody"><div><p>Attempt to convert x to an mpf or mpc losslessly. If x is an mpf or mpc,
return it unchanged. If x is an int, create an mpf with sufficient 
precision to represent it exactly.</p>
<p>If x is a decimal or str, just convert it to an mpf with the current 
working precision (perhaps this should be done differently...)</p>
</div></div>
            </div>
            <div class="function">
            <div class="functionHeader">def <a name="sympy.thirdparty.mpmath.mpmath._convert">_convert(x):</a></div>
            <div class="functionBody"><div><p>Convet x to mpf data</p>
</div></div>
            </div>
            <div class="function">
            <div class="functionHeader">def <a name="sympy.thirdparty.mpmath.mpmath.make_mpf">make_mpf(tpl, construct=object.__new__, cls=mpf):</a></div>
            <div class="functionBody"><div><p>Create mpf verbatim from a given tuple of data.</p>
</div></div>
            </div>
            <div class="function">
            <div class="functionHeader">def <a name="sympy.thirdparty.mpmath.mpmath.make_mpc">make_mpc(tpl, construct=object.__new__, cls=mpc):</a></div>
            <div class="functionBody"><div class="undocumented">Undocumented</div></div>
            </div>
            <div class="function">
            <div class="functionHeader">def <a name="sympy.thirdparty.mpmath.mpmath.sqrt">sqrt(x):</a></div>
            <div class="functionBody"><div><p>For real x &gt;= 0, returns the square root of x. For negative or 
complex x, returns the principal branch of the complex square root of 
x.</p>
</div></div>
            </div>
            <div class="function">
            <div class="functionHeader">def <a name="sympy.thirdparty.mpmath.mpmath.hypot">hypot(x, y):</a></div>
            <div class="functionBody"><div><p>Returns the Euclidean distance sqrt(x*x + y*y). Both x and y must be 
real.</p>
</div></div>
            </div>
            <div class="function">
            <div class="functionHeader">def <a name="sympy.thirdparty.mpmath.mpmath.ef">ef(name, real_f, complex_f, doc):</a></div>
            <div class="functionBody"><div class="undocumented">Undocumented</div></div>
            </div>
            <div class="function">
            <div class="functionHeader">def <a name="sympy.thirdparty.mpmath.mpmath.tan">tan(x):</a></div>
            <div class="functionBody"><div><p>Returns the tangent of x.</p>
</div></div>
            </div>
            <div class="function">
            <div class="functionHeader">def <a name="sympy.thirdparty.mpmath.mpmath.tanh">tanh(x):</a></div>
            <div class="functionBody"><div><p>Returns the hyperbolic tangent of x.</p>
</div></div>
            </div>
            <div class="function">
            <div class="functionHeader">def <a name="sympy.thirdparty.mpmath.mpmath.arg">arg(x):</a></div>
            <div class="functionBody"><div><p>Returns the complex argument (phase) of x. The returned value is an mpf 
instance. The argument is here defined to satisfy -pi &lt; arg(x) &lt;= pi.
On the negative real half-axis, it is taken to be +pi.</p>
</div></div>
            </div>
            <div class="function">
            <div class="functionHeader">def <a name="sympy.thirdparty.mpmath.mpmath.log">log(x, b=None):</a></div>
            <div class="functionBody"><div><p>Returns the base-b logarithm of x. If b is unspecified, return the 
natural (base-e) logarithm. log(x, b) is defined as log(x)/log(b). log(0) 
raises ValueError.</p>
<p>The natural logarithm is real if x &gt; 0 and complex if x &lt; 0 or if 
x is complex. The principal branch of the complex logarithm is chosen, for 
which Im(log(x)) = -pi &lt; arg(x) &lt;= pi.</p>
</div></div>
            </div>
            <div class="function">
            <div class="functionHeader">def <a name="sympy.thirdparty.mpmath.mpmath.power">power(x, y):</a></div>
            <div class="functionBody"><div><p>Returns x**y = exp(y*log(x)) for real or complex x and y.</p>
</div></div>
            </div>
            <div class="function">
            <div class="functionHeader">def <a name="sympy.thirdparty.mpmath.mpmath.atan">atan(x):</a></div>
            <div class="functionBody"><div><p>Returns the inverse tangent of x.</p>
</div></div>
            </div>
            <div class="function">
            <div class="functionHeader">def <a name="sympy.thirdparty.mpmath.mpmath.atan2">atan2(y, x):</a></div>
            <div class="functionBody"><div><p>atan2(y, x) has the same magnitude as atan(y/x) but accounts for the 
signs of y and x. (Defined for real x and y only.)</p>
</div></div>
            </div>
            <div class="function">
            <div class="functionHeader">def <a name="sympy.thirdparty.mpmath.mpmath._asin_complex">_asin_complex(z):</a></div>
            <div class="functionBody"><div class="undocumented">Undocumented</div></div>
            </div>
            <div class="function">
            <div class="functionHeader">def <a name="sympy.thirdparty.mpmath.mpmath.asin">asin(x):</a></div>
            <div class="functionBody"><div><p>Returns the inverse sine of x. Outside the range [-1, 1], the result is 
complex and defined as the principal branch value of -i * log(i * x + 
sqrt(1 - x**2)).</p>
</div></div>
            </div>
            <div class="function">
            <div class="functionHeader">def <a name="sympy.thirdparty.mpmath.mpmath._acos_complex">_acos_complex(z):</a></div>
            <div class="functionBody"><div class="undocumented">Undocumented</div></div>
            </div>
            <div class="function">
            <div class="functionHeader">def <a name="sympy.thirdparty.mpmath.mpmath.acos">acos(x):</a></div>
            <div class="functionBody"><div><p>Returns the inverse cosine of x. Outside the range [-1, 1], the result 
is complex and defined as the principal branch value of pi/2 + i * log(i * 
x + sqrt(1 - x**2)).</p>
</div></div>
            </div>
            <div class="function">
            <div class="functionHeader">def <a name="sympy.thirdparty.mpmath.mpmath.asinh">asinh(x):</a></div>
            <div class="functionBody"><div><p>Returns the inverse hyperbolic sine of x. For complex x, the result is 
the principal branch value of log(x + sqrt(1 + x**2)).</p>
</div></div>
            </div>
            <div class="function">
            <div class="functionHeader">def <a name="sympy.thirdparty.mpmath.mpmath.acosh">acosh(x):</a></div>
            <div class="functionBody"><div><p>Returns the inverse hyperbolic cosine of x. The value is given by log(x 
+ sqrt(1 + x**2)), where the principal branch is used when the result is 
complex.</p>
</div></div>
            </div>
            <div class="function">
            <div class="functionHeader">def <a name="sympy.thirdparty.mpmath.mpmath.atanh">atanh(x):</a></div>
            <div class="functionBody"><div><p>Returns the inverse hyperbolic tangent of x. Outside the range [-1, 1], 
the result is complex and defined as the principal branch value of 
(log(1+x) - log(1-x))/2.</p>
</div></div>
            </div>
            <div class="function">
            <div class="functionHeader">def <a name="sympy.thirdparty.mpmath.mpmath.rand">rand():</a></div>
            <div class="functionBody"><div><p>Return an mpf chosen randomly from [0, 1).</p>
</div></div>
            </div></body>
        